$11^{2}_{22}$ - Minimal pinning sets
Pinning sets for 11^2_22 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_22 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 128
of which optimal: 1
of which minimal: 1
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.89692
on average over minimal pinning sets: 2.0
on average over optimal pinning sets: 2.0
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 5, 8}
4
[2, 2, 2, 2]
2.00
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
4
1
0
0
2.0
5
0
0
7
2.4
6
0
0
21
2.67
7
0
0
35
2.86
8
0
0
35
3.0
9
0
0
21
3.11
10
0
0
7
3.2
11
0
0
1
3.27
Total
1
0
127
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,6,7,7],[0,7,7,8],[0,5,1,1],[1,4,8,6],[2,5,8,8],[2,3,3,2],[3,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[3,12,4,1],[2,18,3,13],[11,6,12,7],[4,10,5,9],[1,14,2,13],[14,17,15,18],[7,15,8,16],[5,10,6,11],[16,8,17,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,4,-10,-5)(17,6,-18,-7)(7,2,-8,-3)(3,8,-4,-9)(1,10,-2,-11)(15,18,-16,-13)(12,13,-1,-14)(14,11,-15,-12)(5,16,-6,-17)
Edge permutation $\epsilon=$ (-1,1)(-2,2)(-3,3)(-4,4)(-5,5)(-6,6)(-7,7)(-8,8)(-9,9)(-10,10)(-11,11)(-12,12)(-13,13)(-14,14)(-15,15)(-16,16)(-17,17)(-18,18)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,-11,14)(-2,7,-18,15,11)(-3,-9,-5,-17,-7)(-4,9)(-6,17)(-8,3)(-10,1,13,-16,5)(-12,-14)(-13,12,-15)(2,10,4,8)(6,16,18)
Multiloop annotated with half-edges
11^2_22 annotated with half-edges